What equals 126 in multiplication?

Steps to Solve

1. Identify the number to factor We need to find the factors of 126. This means we will look for pairs of numbers that multiply to give 126.

2. Start with 1 and the number itself The first factor pair is always 1 and the number itself. So, we have: $$ 1 \times 126 = 126 $$

3. Check for the next integers Next, we will check integers to see if they divide evenly into 126. For example, we will check 2: $$ 126 \div 2 = 63 $$ This gives us another factor pair: $$ 2 \times 63 = 126 $$

4. Continue checking integers We keep checking consecutive integers. The next number is 3: $$ 126 \div 3 = 42 $$ This gives us another factor pair: $$ 3 \times 42 = 126 $$

5. Continue checking up to the square root We can continue this process for numbers up to the square root of 126 (approximately 11.2), checking integers like 4, 5, 6, 7, 8, 9, 10, and 11.

Continuing on:

• For 6: $$ 126 \div 6 = 21 $$ so $$ 6 \times 21 = 126 $$
• For 7: $$ 126 \div 7 = 18 $$ so $$ 7 \times 18 = 126 $$
• For 9: $$ 126 \div 9 = 14 $$. so $$ 9 \times 14 = 126 $$

6. Compile all factor pairs After checking all possible integers, we compile our factor pairs. The complete list of factors of 126 is:

• $(1, 126)$
• $(2, 63)$
• $(3, 42)$
• $(6, 21)$
• $(7, 18)$
• $(9, 14)$